Problem: Rewrite as a simplified fraction. ${3.4\overline{3} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 343.3333...\\ 10x &= 34.3333...\end{align*}}$ Subtracting the two equations, we have: ${90x = 309}$ ${x = \dfrac{309}{90}} $ ${x = \dfrac{103}{30}} \text{or} {3 \dfrac{13}{30}}$